Resumen de The Shapes of Coordination Polyhedra
The shapes of coordination polyhedra can be related to their moments of inertia and the shapes of their momental ellipsoids, which may be spherical (a = b = c), prolate (a > b = c), oblate (a = b > c), or asymmetric (a _ b _ c). The shape of the momental ellipsoid of a given coordination polyhedron can, in turn, be related to the spatial distributions of the atomic orbitals used for the corresponding hybrid orbitals as indicated by their magnetic quantum numbers (m). In this connection possible atomic orbital hybridizations for coordination numbers five through eight are obtained by adding or subtracting orbitals from the spherical four-orbital sp3 and nine-orbital sp3d5 manifolds, respectively. Thus the five-coordinate prolate D3h trigonal bipyramid and oblate C4v square pyramid arise by adding the prolate z2 and oblate x2 - y2 orbitals, respectively, to a spherical four-orbital sp3 manifold. The eight-coordinate oblate D4d square antiprism and prolate bisdisphenoid (D2d dodecahedron) arise by subtracting the prolate z2 and oblate x2 - y2 orbitals, respectively, from a spherical nine-orbital sp3d5 manifold. Six-coordinate polyhedra are formed by adding pairs of d orbitals to the spherical sp3 manifold with the pairs (x2 - y2,z2), (xz, z2), (xy,x2 - y2), and (xy,xz) giving the spherical Oh octahedron, asymmetric C2v bicapped tetrahedron, oblate C5v pentagonal pyramid, and prolate D3h trigonal prism, respectively. The seven-coordinate D5h pentagonal bipyramid, C3v capped octahedron, and C3v and C2v capped trigonal prisms can arise by subtractions of various d orbital pairs from the spherical nine-orbital sp3d5 manifold. However, subtracting the (x2 - y2,z2) d orbital pair from the sp3d5 manifold gives the seven orbitals of the spd set which generate eight cubic hybrids of Oh symmetry when mixed with the f(xyz) orbital.
